Function to fit the Bayesian fixed- and random-effects meta-analytic models with or
without moderators. Models are designed to include non-informative priors.
a data list containing information on observed data (including moderators). See
'details'.
outcome
type of outcome that needs to be specified. For binary, continuous and count data,
bin, ctns and count need to be specified, respectively.
model
type of model that needs to be specified. See 'details'.
type
model type—either fixed-effects (fix) or random-effects model(ran)
needs to be specified.
n.iter
number of iterations to be used in the simulation (default is 10000)
n.burnin
number of burn-in to be used in the simulation (default is 5000)
n.samples
The total number of MCMC simulations saved (including thinning). Default at 1000
n.chains
number of Markov chains to be used in the simulation (default is 2)
model.file
Name of the text file to which the model is saved
Details
Specifying the data
The function can be used to evaluate odds ratios (or log odds ratios), mean difference
and incidence rate ratios (or log incidence rate ratios). Users need to specify a list
of data to be used in the function. For binary data, events out of case and control arm
and sample size of case and control arm need to be listed. For continuous data, mean
and standard errors of case and control arm need to be listed if information is
available. However, if only mean difference and variance can be retrieved from each
study, users need to list mean difference and precision (inverse of variance). Notice
that information of all the studies need to be provided in the same format for the
function to work properly. For example, the function cannot work if some of the studies
provide mean and standard errors of the two arms while the rest studies provide mean
difference and variance. For count data, total number of events in the follow-up period
of case and control arm, total follow-up person-time in case and control arm should
be listed.
If additional impacts of a variable or more than one variable are observed (when
meta-regression is expected to be used), users need to provide a matrix with each column
either containing a dummy variable or a continuous variable. In case that categorical
variables (i.e. ethnicity, age band) are observed and included, users need to first
choose a 'baseline' category as reference and then create dummies for each of the rest
categories.
Model selection
Apart from 'null' models which apply Bayesian methods to obtain study-specific without
pooling-effects, there are 22 models included in this package for pooling study-specific
estimates together and producing summary estimate. The number of models designed for
binary, continuous and count data are 8, 8 and 6, respectively. The model selection
process for binary and count data requires users to specify not only whether
meta-analysis or meta-regression is wanted but also the priors to be used.
For binary data, normal and Student t-distribution priors for summary estimates (on log
scale) can be selected and it is indicated that Student t-distribution has heavier tails
and is therefore more robust to outliers. The argument 'model' here includes 4 options
— std.norm, std.dt, reg.norm, reg.dt.
For continuous data, rather than specifying prior, users need to select whether all
studies included report mean and standard errors of two arms separately or only mean
difference and variance as discussed above in the 'Specifying the data' section. The
argument 'model' here includes 4 options— std.ta, std.mv, reg.ta,
reg.mv ('model' ending with 'ta' represents 'two arms' and ending with 'mv'
represents 'mean and variance').
For count data, uniform and half-Cauchy distribution priors for the variability of
summary estimates (on log scale) can be selected. It is suggested that half-Cauchy
distribution has heavier tails and allows for outliers and accommodates small variances
closing to zero. It should be noticed that there is no need to specify priors for
fixed-effects models for count data. The argument 'model' here includes 6 options
— std, std.unif, std.hc, reg, reg.unif,
reg.hc.
In conjunction with the argument 'type'— fix or ran, users can select
the specific model wanted for a certain type of data.
Value
mod
A rjags object with the results of the model
params
a list of monitored parameters to be saved
data
the original dataset
inits
a list with n.chains elements, with each element itself being a
list of starting values for the model or a function generating initial values
outcome
selected type of outcome (i.e. bin/ctns/count)
type
selected type of model (either fixed-/random-effects)
model
selected model with specific priors
mod0
independent model without pooling effects
Author(s)
Tao Ding
Gianluca Baio
References
Baio, G.(2012) Bayesian methods in health economics. Chapman Hall, CRC.
Welton, N.J., Sutton, A.J., Cooper, N., Abrams, K.R. & Ades, A.E. (2012) Evidence
synthesis for decision making in healthcare. Chichester, UK: John Wiley & Sons,
Ltd.
Examples
### Read and format the data (binary)
data = read.csv(url("http://www.statistica.it/gianluca/bmeta/Data-bin.csv"))
### List data for binary outcome (for meta-analysis)
d1 <- data.list <- list(y0=data$y0,y1=data$y1,n0=data$n0,n1=data$n1)
### List data for binary outcome when there is a covariate (for meta-regression)
d1 <- data.list <- list(y0=data$y0,y1=data$y1,n0=data$n0,n1=data$n1,X=cbind(data$X0))
### Select fixed-effects meta-analysis with normal prior for binary data
m1 <- bmeta(d1, outcome="bin", model="std.norm", type="fix",n.iter=100)
### Select random-effects meta-regression with t-distribution prior for binary
### data
m2 <- bmeta(data.list, outcome="bin", model="reg.dt", type="ran",n.iter=100)
### Read and format the data (continuous)
data = read.csv(url("http://www.statistica.it/gianluca/bmeta/Data-ctns.csv"))
### List data for continuous outcome for studies reporting two arms separately
### (for meta-analysis)
d1 <- data.list <- list(y0=data$y0,y1=data$y1,se0=data$se0,se1=data$se1)
### List data for continuous outcome for studies reporting mean difference and
### variance with a covariate (for meta-regression)
d2 <- data.list2 <- list(y=data$y,prec=data$prec,X=cbind(data$X0))
### Select fixed-effects meta-analysis with studies reporting information of
### both arm for continuous data
m1 <- bmeta(data.list, outcome="ctns", model="std.ta", type="fix",n.iter=100)
### Select random-effects meta-regression with studies reporting mean difference and
### variance only for continuous data
m2 <- bmeta(data.list2, outcome="ctns", model="reg.mv", type="ran",n.iter=100)
### Read and format the data (count)
data = read.csv(url("http://www.statistica.it/gianluca/bmeta/Data-count.csv"))
### List data for count outcome (for meta-analysis)
d1 <- data.list <- list(y0=data$y0,y1=data$y1,p0=data[,6],p1=data[,10])
### List data for count outcome when there is a covariate (for meta-regression)
d2 <- data.list <- list(y0=data$y0,y1=data$y1,p0=data[,6],p1=data[,10],X=cbind(data$X0))
### Select fixed-effects meta-analysis for count data
m1 <- bmeta(d1, outcome="count", model="std", type="fix",n.iter=100)
### Select random-effects meta-analysis with half-Cauchy prior for count data
m2 <- bmeta(d1, outcome="count", model="std.hc", type="ran",n.iter=100)
### Select random-effects meta-regression with uniform prior for count data
m3 <- bmeta(d2, outcome="count", model="reg.unif", type="ran",n.iter=100)